The open string sounds out more or less properly (though it tends to go 'harmonic', which seems like it's probably related to the problem). On the higher frets, it lacks sustain. It sounds dull and 'weird' (like it tries to produce two notes at once, not sure how else to explain this), and the sustain is almost zero.
I have tried different strings, to no avail (exact same result). The bridge/saddle and nut seem undamaged. The fret wire looks alright on all frets, including the ones most affected by this problem.
The other strings are all fine, and I don't see any difference in any of these aspects between them and the G string. I would expect the string to hit something it shouldn't, but after studying it carefully I don't see it hitting fret wire on other frets or anything. And again, there is no difference between the G string and the others that I can see.
What could cause problems like this one, if not any of these factors?